The holes are there because the grubs pupated into June bugs and crawled out of the ground. The grubs are no longer there.

Nematodes are the best organic solution for grubs. However, before spending the money, make sure you have grubs. If you don't have dead patches of lawn, you probably don't have grubs. In about a month would be the best time to apply nematodes. They need damp soil to survive, just like earthworms.

Grubs in the lawn and grubs in compost are two totally different creatures. The first causes harm and the second does not. Compost grubs are much larger than lawn grubs.